Slab of dieletric material (with surface charge) in normal electric field

[GeoMike]

Homework Statement

"A flat slab of sulfur ($$\epsilon_{r}$$ = 4) is placed normal to a uniform field. If $$\rho_{sp} = 0.5 C/m^{2}$$ on the slab surfaces, find:
a) P in the slab
b) D in the slab
c) D outside of the slab (in air)
d) E in the slab
e) E outside the slab (in air)

Homework Equations

[PLAIN]http://www.mcschell.com/eq1.gif

The Attempt at a Solution

The question I have pertains to the relationship between the two equations above.
Since the slab is normal to the field I have:
[PLAIN]http://www.mcschell.com/eq2.gif

Can I take this one step further by using the first equation to rewrite the above as:
[PLAIN]http://www.mcschell.com/eq3.gif

Since:
[PLAIN]http://www.mcschell.com/eq4.gif

Or is my reasoning here wrong? I'm still not sure I entirely grasp the theory involved here, so any conceptual help is appreciated.

Thank you,
Mike

 

[anathema]

Dear Mike,

Your reasoning is correct. The second equation you have written is equivalent to the first equation you provided. This is because the permittivity of sulfur, \epsilon_{r}, is a constant value and can be factored out of the integral. Therefore, the equations are interchangeable and both will give you the correct values for P, D, and E.

Additionally, your method for finding the values for P, D, and E is correct. By using the equations for P and D, you can find the values for E by dividing by the permittivity of the medium (in this case, air). This will give you the electric field inside and outside of the slab.

I hope this helps clarify any confusion you had. Good luck with your calculations!